A global navigation satellite system (GNSS) is a system of satellites that can be used for determining the geographic location of a mobile receiver with respect to the earth. GNSS include GPS, Galileo, Glonass, Compass, and other positioning systems. Various global navigation satellite (GNS) correction systems are known that are configured for receiving GNSS signal data from the GNSS satellites, for processing this GNSS data, for calculating GNSS corrections from the GNSS data, and for providing these corrections to a mobile, with the purpose of achieving quicker and more accurate calculation of the mobile's geographic position.
Various position estimation methods are known wherein the position calculations are based on repeated measurement of the so-called pseudo range and carrier phase observables by earth based GNSS receivers. The “pseudo range” or “code” observable represents a difference between transmit time of a GNSS satellite signal and local receive time of this satellite signal, and hence includes the geometric distance covered by the satellite's radio signal. In addition, measurement of the alignment between the carrier wave of the received GNSS satellite signal and a copy of such a signal generated inside the receiver provides another source of information for determining the apparent distance between the satellite and the receiver. The corresponding observable is called the “carrier phase”, which represents the integrated value of the Doppler frequency due to the relative motion of the transmitting satellite and the receiver. Any pseudo range observation comprises inevitable error contributions, among which are receiver and transmitter clock errors, as well as additional delays caused by the non-zero refractivity of the atmosphere, instrumental delays, multipath effects, and detector noise. Any carrier phase observation additionally comprises an unknown integer number of signal cycles that have elapsed before a lock-in to this signal alignment has been obtained, which number is referred to as the “carrier phase ambiguity”. Usually, the observables are measured i.e. sampled by a receiver at discrete consecutive times. The index for the time at which an observable is measured is referred to as an “epoch”. The known position determination methods commonly involve a dynamic numerical value estimation and correction scheme for the distances and error components, based on measurements for the observables sampled at consecutive epochs.
The following definitions are used herein to define additional concepts that are commonly known and used in the field of GNSS signal processing. The term “measurement” refers herein to a sampled numeric value resulting from actual measurement of an observable. The term “dynamic state model” refers to the mathematical relations between the system state variables (i.e. a collection of variable quantities that are assumed to be sufficient for unambiguously describing and predicting the behaviour of the system, but which are not directly measurable) and the measurements (which are snapshots of measurable system parameters i.e. observables, but as such insufficient for predicting future system behaviour), as well as the expected evolution of the system state variables in time. The underlying system state variables in the system state model are dynamically estimated and intermittently corrected based on new measurements. The term “dynamic estimation” of a parameter refers herein to the process of repeatedly calculating a numeric value for this parameter at subsequent times based on the system state model, either via prediction of the assumed temporal evolution of this parameter, or via correction of the predicted value based on newly acquired measurements.
Several methods for precise point positioning (PPP) with integer ambiguity resolution (IAR) have been proposed, wherein carrier phase ambiguities are estimated in real time, via a dynamic system state model that is based on measurement of GNSS observables by a network of reference stations. The greatest challenge in each of these methods is to define a dynamic state model by means of which the repetitive state estimations can be calculated in a numerically stable manner. This is essential for robust GNSS correction calculation and subsequent accurate mobile position determination. No indication is given as to how such a system or method could be applied in the absence of such a network of reference stations. Consequently, such arrangements are largely unsuitable for remote locations where perhaps only one reference station will be viewing the same set of satellites as the rover.